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Logic
Trivium
169
Classics
9th Grade
04/15/2013
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Term
Subalterns
 Definition
Are A and I as well as E and O. They have the same quality but differ either in being partial instead of total or in being contingent instead of necessary.
Term
Oppositions
 Definition
Have the same matter (subject and predicate) but differ in form (quality, quantity, modality, or in two of these).
Term
Contradictories
 Definition
A (all S is/must be P) and O (some S is not/may not be P) as well as E (no S is/may be P) and I (some S is/may be P). They differ in quality and either quantity or modality. There is no middle ground between them.
Term
Rule for contradictories
 Definition
One must be true and the other false.
Term
Contraries
 Definition
Are A (all S is/must be P) and E (no S is/can be P). They differ in quality and are either total in quantity or necessary in modality. There is a middle ground between them.
Term
Rule for contraries
 Definition
Both cannot be true, but both may be false.
Term
Subcontraries
 Definition
Are I (some S is/may be P) and O (some S is not/may not be P). They differ in quality and are either partial in quantity or contingent in modality.
Term
Rule for subcontraries
 Definition
Both cannot be false, but both may be true.
Term
Subalterns
 Definition
Are A (all S is/must be P) and I (some S is/may be P) as well as E (no S is/can be P) and O (some S is not/may not be P). They have the same quality but differ in being partial instead of total or in being contingent instead of necessary.
Term
Rule for subalterns
 Definition
If the total or necessary proposition is true, the partial or contingent must be true; but if the former is known to be false, the value of the latter is unknown.

And if the partial or contingent proposition is false, the total or necessary must be false; but if the former is known to be true, the value of the latter is unknown.
Term
A
 Definition
Total or necessary affirmation.
S a P
All S is P
S must be P
Term
E
 Definition
Total or necessary negation.
S e P
No S is P
S cannot be P
Term
I
 Definition
Partial or contingent affirmation.
S i P
Some S is P
S may be P
Term
O
 Definition
Partial or contingent negation.
S o P
Some S is not P
S may not be P
Term
Distribution of
S a P
 Definition
S is distributed while P is not.
Term
Distribution of
S e P
 Definition
Both are distributed.
Term
Distribution of
S i P
 Definition
Neither is distributed.
Term
Distribution of
S o P
 Definition
S is not distributed, but P is.
Term
Distribution of Predicates
 Definition
Occurs in negative propositions.
Term
Categorematic words
 Definition
From the 10 categories of being:

Substantives (nouns and pronouns)

Primary Attributives ( verbs, verbals, adjectives)

Secondary Attributives (attributes of attributes: adverbs)
Term
Syncategorematic Words
 Definition
Words significant only with other words:

Definitives (articles and pronomials)

Connectives (prepositions and conjunctions)

Pure Copula
Term
10 Categories
 Definition
Substance
Quantity
Quality
Relation
Action
Passion
When
Where
Posture
Habiliment
Term
Contradictories
 Definition
A and O; E and I
Term
Contraries
 Definition
A and E
Term
Subcontraries
 Definition
I and O
Term
Subalterns
 Definition
A and I; E and O
Term
Opposition of singular empirical propositions for categorical forms
 Definition
Is achieved through a difference of quality alone and is restricted to contradiction:

A Mary is tall
E Mary is not tall
Term
Opposition of singular empirical propositions in modal forms
 Definition
Includes all four relations:

A Mary must be nice
E Mary cannot be nice
I Mary may be nice
O Mary may not be nice
Term
Given E is true
 Definition
Then I is false,
A is false,
O is true
Term
Given E is false
 Definition
Then I is true,
A and O are unknown
Term
Given I is true
 Definition
Then E is false,
A and O are unknown
Term
Given I is false
 Definition
Then E is true,
A is false,
O is true
Term
Given O is true
 Definition
Then A is false,
E and I are unknown
Term
Given O is false
 Definition
Then A is true,
E is false
Term
Obversion
 Definition
Changes a proposition's quality (from affirmation to negation or negation to affirmation) and predicate (from P to P' = non-P) but not the meaning.
Term
Obversion of A
 Definition
S a P → S e P'

All voters are citizens→No voters are noncitizens
Term
Obversion of E
 Definition
S e P→S a P'
No Jews are Muslims→All Jews are non-Muslims
Term
Obversion of I
 Definition
S i P→S o P'


Some chairs are comfy→Some chairs are not comfy
Term
Obversion of O
 Definition
S o P→S i P'
Some pupils listen→Some pupils don't listen
Term
Conversion
 Definition
Reverse the subject and predicate, change the quantity if need be, but don't change the quality.

No term may be distributed in the converse that was undistributed in the original proposition.
Term
Converting S a P
 Definition
To P i S

To P a S, but only when P is the definition or property of S, i.e., when it is distributed through the matter.

E.g. Man is a rational animal. A rational animal is man.

Otherwise beware of distributing P in affirmative propositions.
Term
Converting S e P
 Definition
To P e S
Term
Converting S i P
 Definition
To P i S
Term
Converting S o P
 Definition
It may be true to convert to P o S, but the original S is not distributed and yet becomes a P in a negative proposition (and so is then distributed incorrectly).

The truth of P o S is an accident of matter and the proposition is formally invalid.
Term
Contrapositive
 Definition
The quality of a proposition is changed and the predicate is converted to its contradictory
Term
Inverse
 Definition
A proposition that uses the contradictory of the subject and the predicate of the original proposition.
Term
Eductions of S a P:
All voters are citizens.
 Definition
Obverse - S e P':
No voters are noncitizens.

Partial contrapositive - P' e S:
No noncitizens are voters.

Full contrapositive - P' a S':
All noncitizens are nonvoters.

Full inverse - S' i P':
Some nonvoters sre noncitizens.

Partial inverse - S' o P:
Some nonvoters are not citizens.

Converse - P i S:
Some citizens are voters.

Obverted converse - P o S':
Some citizens are not nonvoters.
Term
Eductions of S e P:
No Jews are Muslims.
 Definition
Obverse - S a P:
All Muslims are non-Jews.

Partial contrapositive - P' i S:
Some non-Jews are Muslims.

Full contrapositive - P' o S':
Some non-Jews are not non-Muslims.

Converse - P e S:
No Jews are Muslims.

Obverted converse - P a S':
All Jews are non-Muslims.

Partial inverse - S' i P:
Some non-Muslims are Jews.

Full inverse - S' o P':
Some non-Muslims are not non-Jews.
Term
Eduction of forms
 Definition
Alternately and successively use obversion (change quality and substitute P with P') and conversion (reverse S and P and don't change quality).
Once you arrive at S o P, return to the original proposition and begin with the opposite process of eduction. E.g., if you began with obversion, then use conversion.
Term
Eduction of S i P:
Some chairs are uncomfy.
 Definition
Obverse - S o P':
Some chairs are not uncomfy.

Coverse - P i S:
Some comfy things are chairs.

Obverted coverse - P o S':
Some comfy things are not nonchairs.
Term
Eduction of S o P:
Some kids are not attentive.
 Definition
Obverse - S i P':
Some kids are inattentive.

Partial contrapositive - P' i S:
Some inattentive beings are kids.

Full contrapositive - P' o S':
Some inattentive beings are not nonkids.
Term
Eduction of S a P with P fully distributed, i. e., when P is either the definition or a property of S:

All men are rational animals.
 Definition
Converse - P a S:
All rational animals are men.

Obverted converse- P e S':
No rational animals are nonmen.

Partial inverse - S' e P:
No nonmen are rational animals.

Full inverse - S' a P':
All nonmen are nonrational animals.

Full contrapositive - P' a S':
All nonrational animals are nonmen.

Partial contrapositive - P' e S:
No nonrational animals are men.

Obverse - S e P':
No men are nonrational animals.

Original - S a P:
All men are rational animals.
Term
Eduction by added determinants
 Definition
S is P; therefore Sa is Pa.
"a" must affect S and P to the same degree and respect.

Of degree:
Original: An ant (S) is an animal (P).
Invalid: a large (a) ant (S) is a large (a) animal (P).
Valid: a small (a) ant (S) is a small (a) animal (P).

Of respect:
Original: A contralto is a woman.
Invalid: a low contralto is a low woman.
Valid: a blonde contralto is a blonde woman.
Term
Eduction by omitted determinants
 Definition
S is Pa; therefore S is P. A subject included in a more determined predicate is necessarily included in that predicate when it is less determined.

E.g., Socrates is a rational animal; therefore Socrates is an animal.
Term
Eduction by converse relation
 Definition
S r1 P; therefore P r2 S.
(r1 and r2=copulas with correlative modifiers rather than simple copulas.)

Relative terms necessarily imply their correlatives (e.g., genus and species), so the subject and predicate with a relative copula may be transposed if the relative copula is supplanted by its correlative.

Original: Aristotle (S) taught (r1) Alexander the Great (P).
Valid inference: Alexander the Great (P) was taught (r2) by Aristotle (S).

Original: A (S) is greater (r1) than B (P).
Valid inference: B (P) is less (r2) than A (S).

Original: Lily (S) is a species (r1) of flower (P).
Valid inference: Flower (P) is a genus (r2) of lily (S).
Term
Predicables
 Definition
Classification of relations a predicate may be affirmed to have to a subject
Term
List of predicables
 Definition
Species
Genus
Differentia
Definition
Property
Accident
Term
The four relations of propositions
 Definition
Conjunction
Opposition
Eduction
Syllogism
Term
Rules of conjunctional propositions
 Definition
True only when every proposition conjoined is true

False if any one of the propositions conjoined is false

Probable if at least one of the propositions conjoined is propable and none are false
Term
Syllogism
 Definition
Two propositions (called premises) having one term in common leading to a third proposition (called the conclusion) in which the common term (called the middle term, M) does not appear.

A bat (S) is a mammal (M)
No bird (P) is a mammal (M)
A bat (S) is not a bird (P)
Term
Matter of syllogism
 Definition
Start with the conclusion:

Minor term is the subject (S) of the conclusion

Major term is the predicate (P) of the conclusion

Conclusion:
A bat (S) is not a bird (P)

So the Minor Premise is:
A bat (S) is a mammal (M)

The Major Premise:
No bird (P) is a mammal (M)
Term
Rule 1 of syllogisms
 Definition
It must contain 3 and only 3 terms.
Term
Rule 2 of syllogisms
 Definition
It must contain 3 and only 3 propositions
Term
Rule 3 of syllogisms
 Definition
The middle term must be distributed in at least one of the premises
Term
Rule 4 of syllogisms
 Definition
No term may be distributed in the conclusion which wasn't distributed in its own premise
Term
Rule 5 of syllogisms
 Definition
From 2 negative premises no conclusion can be drawn
Term
Rule 6 of syllogisms
 Definition
If one premise is negative, the conclusion must be negative. Or, in order to prove a negative conclusion, one premise must be negative
Term
Rule 7 of syllogisms
 Definition
From two partial or singular or contingent premises, no conclusion can be drawn. See rules 3, 5, and 6.
Term
Rule 8 of syllogisms
 Definition
If one premise is partial, the conclusion must be partial. See rules 3 and 4.
Term
Rule 9 of syllogisms
 Definition
If one premise is contingent, thr conclusion must be contingent.
Term
Rule 10 of syllogisms
 Definition
If one or both premises are empirical, the conclusion must be empirical.
Term
Mood of a syllogism
 Definition
It is designated by the A, E, I or O forms of propositions and their order.

With 4 propositional forms we get 16 possible combos: AA, AE, AI, AO, EA, EE, EI, EO, IA, IE, II, IO, OA, OE, OI, OO.

Rule 5 eliminates EE, EO, OE, and OO.

Rule 7 eliminates II, IO, OI, and (again) OO.

Special rules (tba) eliminate EI.
Term
8 standard combos of premises
 Definition
AAA (AAI)
AEE (AEO)
AII
AOO
EAE (EAO)
IAI
IEO
OAO
Term
Figure of syllogism
 Definition
Determined by position of middle term in the premises: is it the subject or predicate of the minor or major term?
Term
Figure 1
 Definition
The middle term is the predicate of the minor premise and the subject of the major premise:

S__M
M__P
S__P

M__P
S__M
S__P
Term
Figure 2
 Definition
The middle term is the predicate of both premises:

S__M
P__M
S__P

P__M
S__M
S__P
Term
Figure 3
 Definition
The middle term is the subject of both:

M__S
M__P
S__P

M__P
M__S
S__P
Term
Figure 4
 Definition
The middle term is the subject of the minor premise and the predicate of the major:

M__S
P__M
S__P

P__M
M__S
S__P
Term
The mood and figure of:
1.A bat (S) is a mammal (M).
2.No bird (P) is a mammal (M).
→3.A bat (S) is not a bird (P).
 Definition
1.A
2.E
3.E
Figure 2
Term
Distribution of terms
 Definition
See if the middle term is distributed in at least one premise (rule 3).

See if P or S is distributed in the conclusion but undistributed in its premises (rule 4).

1. A bat (S) is (A) a mammal (M): S is distributed, M is not.

2. No bird (P) is (E) a mammal (M): both P and M are distributed.

3. A bat (S) is not (E) a bird (P): both are distributed. Valid.
Term
Enthymeme
 Definition
A syllogism omitting one proposition, either the major premise, the minor premise, or conclusion.
Term
To find the conclusion of an enthymeme
 Definition
Look for "because," "for," or "since." These introduce a premise and therefore the other proposition is the conclusion.

Look for therefore, consequently, or accordingly, which introduce a conclusion.

Look for and or but, which connect two premises and indicate that the proposition omitted is rhe conclusion.
Term
Validity of an enthymeme
 Definition
If it is valid in one expansion, it's valid.

If it is invalid in the first expansion, expand it in the alternate figure to see if it can become valid. For example:

An oak (S-D) is a plant (P-U) because it (S-D) is a tree (M-U).

Expansion B:
An oak (S-D) is a tree (M-U).
All plants (P-D) are trees (M-U).
An oak (S-D) is a plant (P-U).

This is invalid Figure 2 syllogism because of an undistributed (U) middle term (M).

So Expansion A:
An oak (S-D) is a tree (M-U).
A tree (M-D) is a plant (P-U).
An oak (S-D) is a plant (P-U).

This is a valid Figure 1 syllogism.
Term
Typical enthymeme
 Definition
Has the conclusion (with S and P terms) and one premise stated (with either the S and M or P and M terms).

Either the premise with the minor term S is missing or the premise with the major term P is missing.
Term
Sorites
 Definition
A chain of enthymemes or abridged syllogisms, in which the conclusion of one syllogism becomes a premise of the next
Term
First type of sorites
 Definition
That in which the conclusion of one syllogism becomes the major premise of the next:

Goclenian sorites (figure 1)
Term
Second type of sorites
 Definition
That in which the conclusion of one syllogism becomes the minor premise of the next:

Aristotelian sorites (figure 1)
Term
Aristotelian sorites;

The first proposition is the minor premise of its syllogism and all the rest are major premises except for the last, which is a conclusion.

The omitted conclusion in each syllogism becomes the minor premise of the following syllogism.
 Definition
Socrates is a man - S a M1
A man is an animal - M1 a M2
(Omitted conclusion and minor premise: Socrates is an animal.)
An animal is an organism - M2 a M3
(Omitted conclusion and minor premise: Socrates is an organism.)
An organism is a body - M3 a M4
(Omitted conclusion and minor premise: Socrates is a body.)
A body is a substance - M4 a P
Socrates is a substance - S a P
Term
Goclenian sorites:

The first proposition is the major premise of its syllogism and all the rest are minor premises, except the last which is a conclusion.

The omitted conclusion in each syllogism becomes the major premise for the following syllogism.
 Definition
A body is a substance - M1 a P
An organism is a body - M2 a M1 (Omitted conclusion and major premise: An organism is a substance.)
An animal is an organism - M3 a M2
(Omitted conclusion and major premise: An animal is a substance.)
A man is an animal - M4 a M3
(Omitted conclusion and major premise: A man is a substance.)
Socrates is a man - S a M4
Socrates is a substance - S a P
Term
Aristotelian sorites expanded
 Definition
Socrates is a man - S a M1
Man is an animal - M1 a M2
Socrates is an animal - S a M2

Socrates is an animal - S a M2
An animal is an organism - M2 a M3
Socrates is an organism - S a M3

Socrates is an organism - S a M3
An organism is a body - M3 a M4
Socrates is a body - S a M4

Socrates is a body - S a M4
A body is a substance - M4 a P
Socrates is a substance - S a P
Term
Goclenian sorites expanded
 Definition
A body is a substance - M1 a P
An organism is a body - M2 a M1
An organism is a substance - M2 a P

An organism is a substance - M2 a P
An animal is an organism - M3 a M2
An animal is a substance - M3 a P

An animal is a substance - M3 a P
A man is an animal - M4 a M3
A man is a substance - M4 a P

A man is a substance - M4 a P
Socrates is a man - S a M4
Socrates is a substance - S a P
Term
Aristotelian sorites rules
 Definition
1. Only the last premise may be negative.

2. Only the first (minor) premise may be partial, contingent or singular.
Term
Goclenian sorites rules
 Definition
1. Only the first premise can be negative.

2. Only the last (minor) premise may be partial, contingent or singular.
Term
Epicheirma
 Definition
An abridged polysyllogism combining any figures, one whose premises is an enthymeme.
Term
Double epicheirema
 Definition
Both premises are enthymemes
Term
Example of single epicheirma
 Definition
Beefsteak is not stored in the body because it is protein.
Food that is not stored in the body is not fattening.
Beefsteak is not fattening.
Term
Expanded single epicheirma
 Definition
Beefsteak (S) is protein (M).
Protein ( M) is food that is not stored in the body (P).
Beefsteak (S) is food that is not stored in the body (P).

Fig. 4, mood AAA, valid.

Beefsteak (S) is food thay is not stored in the body (M).
Food not stored in the body (M) is not fattening (P).
Beefsteak (S) is not fattening (P).

Fig. 4, mood AEE, valid
Term
Multiple enthymeme v epicheirema
 Definition
The multiple enthymeme has only one conclusion and many reasons supporting it.

The epicheirma has two conclusions and the double has three because they become premises which lead to a third conclusion.
Term
Given A is true
 Definition
The O and E are false, I is true
Term
Given A is false
 Definition
O is true, E and I are unknown
Term
Exame of Analogical inference
 Definition
Sparks (S1) from an electrical machine are electrical charges (P), for they (S1) have rapid motion and conductivity (M):
S1 is P because S1 is M.

Lightening (S2) resembles these sparks (S1) in rapid motion and conductivity (M):
S2 resembles S1 in M.

Lightening (S2) is probably an electrical charge (P):
S2 is probably P.
Term
Validity of Analogical inference
 Definition
Requires that the point of resemblance (M) be a property of P.
Term
Example of Mediate opposition using mediated contraries
 Definition
Mediate Contraries (AE):
X: The witness is lying.
Z': The witness is telling the truth.

An immediate opposition uses Contradictories (AO, EI):
X: The witness is lying.
X': The witness is not lying.
Term
Rules of Mediated Opposition
 Definition
1. The syllogism must be formally valid.

2. The third proposition, Y, must be materially true.
Term
Illustrated Mediated Opposition
 Definition
Mediated Opposition:
The witness is lying.
The witness is telling the truth.

Let X = minor premise
Y = major premise
Z = conclusion

Disputant 1:
X = The witness is lying.
Y = Whoever lies doesn't tell the truth.
Z = The witness is not telling the truth.

Let X' = contradictory of X
Let Z' = contradictory of Z

Disputant 2:
X' = The witness is not lying.
Y = Whoever lies doesn't tell the truth.
Z' = The witness is telling the truth.

Y is the omitted but shared proposition held by disputants 1 and 2 in the mediated opposition.
Term
Relations of Mediated Opposition
 Definition
If Y is materially true:

X (the witness is lying) and Z' (the witness is telling the truth) are mediated contraries (A and E) and both cannot be true, but both can be false.

Z (the witness is not telling the truth) and X' (the witness is not lying) are subcontraries (I and O) and both cannot be false but both may be true.
Term
Syllogistic rules of inference
 Definition
1. If both premises are true, the conclusion is.

2. If the conclusion is false, at least one of the premises must be false.

3. If one or both premises are false, the conclusion is unknown.

4. If the conclusion is true, the value of the premises are unknown.

5. If one or both of the premises are probable, the conclusion can only be probable.

6. If the conclusion is probable, the value of the premises is unknown
Term
Figure 2 special rules
 Definition
Figure 2's middle term, M, is predicate in both premises:
S__M
P__M
S__P

Hence,
1. One premise must be negative to distribute M.

Because a negative premise requires a negative conclusion (rule 6), the major term P will be distributed in the conclusion.

Yet it cannot be distributed in the conclusion without having already been distributed in its own premise. There, however, the major term P is the subject, and only a total or necessary proposition distributes its subject. So

2. The major premise must be total or necessary and so take the mood of either A or E.

So the valid moods of figure 2 are:
AEE, EAE, IEO, OAO.
Term
Figure 1 special rules
 Definition
Figure 1's middle term (M) is the predicate of the minor term (S) and the subject of the major term (P):
S__M
M__P
S__P

Hence,
1. The minor premise (S) must be affirmative.

This is because if the minor premise were negative, the conclusion would be negative (rule 6). But then the major term P would be distributed in the conclusion, and it could not be distributed in the conclusion without also being distributed in its own premise (rule 4). For that to happen, however, would require the major premise to also be negative, and yet two negative premises lead to no conclusion (rule 5).

2. The major premise must be total or necessary to avoid an undistributed middle term, because that term was not distributed in the (affirmative) minor premise.

So the valid moods of figure 1 are:
AAA, AEE, IAI, IEO
Term
Figure 3 special rules
 Definition
Figure 3's middle term (M) is the subject of the minor (S) and major (P) premises:
M__S
M__P
S__P

Hence,
1. The minor premise (S) must be affirmative.

2. Because S is formally undistributed it will be undisturbed in the conclusion, and only partial or contingent propositions have undisturbed subjects. Thus the conclusion is partial and contingent.

So the valid moods of figure 3 are:
AAI, AII, IAI, AEO, AOO, IEO
Term
Figure 4 special rules
 Definition
The middle term is the subject of the minor term (S) and predicate of the major term (P):
M__S
P__M
S__P

1. If the major premise is affirmative, M is undistributed and so must be distributed in the minor (rule 3) where it is subject. So M__S must be total or necessary.

2. If the minor is affirmative, the conclusion must be partial or contingent (rule 2 of fig. 3).

3. If the conclusion is negative, the major premise must be total or necessary (rule 2 of fig. 2).

Moods:
AAI, EAE, AII, AEO, IEO
Term
Figure 1 alone can yield
 Definition
A total or necessary general affirmative proposition as conclusion
Term
Figure 2 can only yield
 Definition
Negative conclusions, unless one premise is a definition.

It's adapted to disproof.
Term
Figure 3 can only yield
 Definition
Partial, singular or contingent conclusions, unless one premise is the definition.

It's adapted to proving exceptions.
Term
Syllogistic reduction
 Definition
A process where a syllogism in an imperfect figure (2, 3 or 4) is expressed as a syllogism of the first figure.

Assumes;
1. Imperfect figures' premises are true.
2. That the first figure is formally valid.
Term
Figure reduction-Valid Moods
 Definition
First Figure:
Barbara (AAA), Celarent (EAE), Darii (AII), Ferio (EIO), que prioris.

Second Figure:
Cesare (EAE), Camestres (AEE), Festino (EIO), Baroco (AOO), secundae.

Third Figure:
Tertia Darapti (AAI), Disamis (IAI), Datisi (AII), Felapton (EAO)
Bocardo (OAO), Ferison (EIO) habet.

Fourth Figure:
Quarta in super addit
Bramantip (AAI), Camenes (AEE), Dimaris (IAI), Fesapo (EAO), Fresison (EIO).

Vowels = mood in traditional order:
Major premise, minor premise, conclusion.

B, C, D, and F names in second to fourth syllogisms can have their moods reduced to the first figure moods whose names begin with the same letter. E.g.,
Camestres (AEE) of the second figure can be reduced to Celarent (EAE) of the first figure.
Term
Mode of reduction to first figure form
 Definition
Barbara (AAA), Celarent (EAE), Darii (AII), Ferio (EIO), que prioris.

Cesare (EAE), Camestres (AEE), Festino (EIO), Baroco (AOO), secundae.

Tertia Darapti (AAI), Disamis (IAI), Datisi (AII), Felapton (EAO)
Bocardo (OAO), Ferison (EIO) habet.

Quarta in super addit
Bramantip (AAI), Camenes (AEE), Dimaris (IAI), Fesapo (EAO), Fresison (EIO).

A name with the letter "s" in it signifies that the vowel preceding it (Disamis-IAI-of the 3rd syllogism) is reduced to the first figure mood (Darii-AII) by simple conversion (reverse subject and predicate).

"P" signifies that the proposition indicated by the proceeding vowel must be converted by limitation (A to I in one case or I to A) to the first figure mood.

"M" signifies premises are to be transposed; "c" by showing that the conclusion in the first figure contradicts a premise given as true in another figure; r, b, l, n, t, d mean nothing.
Term
Reducing Camestres to Celarent (A to B)
 Definition
CaMeStreS (AEE) or A:

All circles (P) are (a) curvilinear (M).
M-Transpose

No square (S) is (e) curvilinear (M).
S-Convert

No square (S) is (e) a circle (P).
S-Convert

Celarent or B:

No curvilinear figure (M) is (E) a square (P).
All circles (S) are (A) curvilinear (M).
No circle (S) is (E) a square (P).
Term
Reduction by "c", per contradictorian propositionem: BoCardo (OAO) to Barbara (AAA)
 Definition
From Barbara, using as premises the A of Bocardo and the contradictory of its conclusion draw the conclusion implicit in these premises:

Bocardo or A:

Some lions (M) are not (o) tame (P).
All lions (M) are (a) animals (S).
Some animals (S) are not (o) tame (P).

Barbara or B:

All animals (M) are (a) tame (P).
All lions (S) are (a) animals (M).
All lions (S) are (a) tame (P).

Because premise O of Bocardo is true and the conclusion of Barbara is its contradictory, that conclusion, though of a valid syllogism, is false. So the matter rather than the form is to blame, meaning one of the premises must be false. And because the minor premise of Barbara was given by Bocardo as true, then its major premise, All animals are tame, must be false. That premise is the contradictory of Bocardo's conclusion, Some animals are not tame, which means that Bocardo's conclusion is true.
Term
Hypothetical syllogism
 Definition
Expresses a conditional relation of propositions
Term
Simple syllogism
 Definition
Expresses a relation of terms
Term
3 term hypothetical proposition's formula
 Definition
If S is M, it is P
Term
4 term hypothetical proposition's formula
 Definition
If B is C, D is E
Term
Reduction of three term hypothetical proposition
 Definition
If S is M, it is P→SM is P
Term
Reduction of four term hypothetical proposition
 Definition
If B is C, D is E→ BC is DE
Term
Hypothetical proposition and its contradictory
 Definition
If a man drinks water, he will die.

If a man drinks water, he will not die.

Taken in relation to the first proposition, which is false, the second, its contradictory, is true, though not by itself.
Term
First of disjunctive propositions
 Definition
1. S is P or Q or R.

The alternatives are:

A) collectively exhaustive
B) mutually exclusive
C) species resulting from division acording to single basis
Term
Second of disjunctive propositions
 Definition
2. S or T or U is P
Term
Third type of disjunctive proposition
 Definition
3. B is C or D is E
Term
Eduction of hypothetical propositions
 Definition
Original: if a tree is a pine, it is necessarily an evergreen.

Obverse: if a tree is a pine, it is necessarily not a nonevergreen.

Partial contrapositive: if a tree is a nonevergreen, it is necessarily not a pine.

Full contrapositive: if a tree is a nonevergreen, it is necessarily a nonpine.

Full inverse: if a tree is a nonpine, it may be a nonevergreen.

Partial inverse: if a tree is a nonpine, it may not be an evergreen.

Converse: if a tree is an evergreen, it may be a pine.

Obverted converse: if a tree is an evergreen, it may not be a nonpine.
Term
Eduction of disjunctive proposition
 Definition
Original: a material substance must be either a gas, liquid or solid.

Converse: a substance that is either a gas, liquid or solid must be a material substance.

Obverted converse: a substance that is either a gas, liquid, or solid cannot be a nonmaterial substance.

Partial inversion: a nonmaterial substance cannot be either a gas, liquid or solid

Full inverse: a nonmaterial substance must be neither a gas, liquid nor solid.

Full contrapositive: a substance that is either neither a gas, liquid nor a solid must be a nonmaterial substance.

Partial contrapositive: a substance that is neither a gas, liquid nor a solid cannot be a material substance.

Obverse: a material substance cannot be neither a gas, liquid nor solid.

Original.
Term
Mixed hypothetical syllogism
 Definition
The major premise is a hypothetical proposition, and the minor premise is a simple proposition
Term
Rules for the mixed hypothetical syllogism
 Definition
The minor premise must either:

1. (Modus ponens - the way of affirmation:) posit the antecedent or

2. (Modus tollens - the way of negation:) sublate the consequent of the major premise (by restating as fact its contradictory).
Term
Example of positing the antecedent: modus ponens
 Definition
Major premise:
(Antecedent) If a man is not honest, (consequent) he is not a fit public officer.

Minor Premise:
(Positing of antecedent) This man is not honest.

Conclusion;
(Positing of consequent) This man is not a fit public officer.
Term
Example of sublating the consequent: modus tollens
 Definition
Major premise:
(Antecedent) If all students were equally competent, (consequent) each would have the same grade in a given course.

Minor premise:
(Sublating of consequent) But each doesn't acquire the same amount of knowledge from a given course.

Conclusion:
(Sublating the antecedent) All students are not equally competent.

The conclusion is the contradictory of the antecedent.
Term
Fallacy of sublating the antecedent
 Definition
If a man drinks poison, he will die.
This man has not drunk poison.
He will not die.

Syllogistically:

Whoever drinks poison (M) will (a) die (P).
This man (S) has not (e) drunk poison (M).
He (S) will not (e) die (P).

P is distributed in the conclusion but not in the major premise, hence the syllogism is invalid.
Term
Fallacy of positing the consequent
 Definition
If a man drinks poison he will die.
This man died.
He must have drunk poison.

Syllogistically:

Whoever drinks poison (P) will (a) die (M).
This man (S) died (a and M).
He (S) must have (a) drunk poison (P).

The middle term is undistributed.
Term
Modus pollens
 Definition
Whenever the minor premise posits the antecedent, the conclusion posits the consequent:

(Major premise;) If A (antecedent) then B (consequent).
(Minor:) A .
(Conclusion;) B.
Term
Modus tollens
 Definition
Whenever the minor premise sublates the consequent, the conclusion sublates the antecedent.

(Major premise:) If A (antecedent) then B (consequent).
(Minor premise:) -B.
(Conclusion:) -A.
Term
Ponendo tollens of a disjunctive syllogism
 Definition
The minor premise posits one alternative, and the conclusion sublates the other.

This woman's missing husband (S) is either living (P) or dead (Q).
He is living (P).
He is not dead (-Q).
Term
Tollendo ponens of disjunctive syllogism
 Definition
The minor premise sublates one alternative, and the conclusion posits the other.

Th soul (S) is either spiritual (P) or material (Q)
The soul is not material (S=-Q)
The soul is spiritual (S=P).
Term
Disjunctive fallacies
 Definition
Formal: Where the minor premise and conclusion both posit and sublate each alternative.

Material: Where the alternatives are not mutually exclusive or not collectively exhaustive.
Term
Dilemma
 Definition
A syllogism with:

1. A disjunctive minor premise

2. A compound hypothetical proposition for its major premise

3. A simple or disjunctive proposition for its conclusion.
Term
Dilemma's moods
 Definition
1. Simple constructive

2. Complex constructive

3. Simple destructive

4. Complex destructive
Term
Fallacies of the dilemma
 Definition
1. False major premise

2. Imperfect disjunction in the minor premise

3. The dilemmatic fallacy, from a shifting point of view
Term
Exposing the dilemma with a false major premise
 Definition
Taking the dilemma by the horns
Term
Exposing the dilemma of the imperfect disjunction in the minor premise
 Definition
Escaping between the horns
Term
Exposing the dilemmatic fallacy
 Definition
Rebutting the dilemma:

Used when the dilemma open to rebutal and the rebutting dilemma contain a formal and material fallacy.

Accept the alternatives in the minor premise of the original dilemma but transpose the consequents of the major premise and change them into contraries.
Term
Constructive dilemma
 Definition
The minor premise posits the two antecedents of the major
Term
Destructive dilemma
 Definition
The minor premise sublates the two consequents of the major premise
Term
Fallacies in dictione
 Definition
1. Equivocation
2. Amphiboly
3. Composition
4. Division
5. Accent
6. Verbal form
Term
Fallacy of equivocation
 Definition
Feathers are light.
Light is the opposite of darkness.
Feathers are the opposite of darkness.
Term
Fallacy of amphiboly
 Definition
Produced by ambiguity of syntax or grammatical structure.

He told his brother that he had won the prize. (Who?)
Term
Fallacy of composition
 Definition
Properties of parts are illicitly predicated of the whole.
Term
Fallacy of division
 Definition
When properties of the whole are illicitly predicated of the parts
Term
Fallacy of verbal form
 Definition
Inspiration and inexplicable: if "in" means "not" in one, it means "not" in the other.
Term
Fallacy of accident
 Definition
A shifting of usage in one term. For example, to shift from first imposition to second:

1st Imposition - Feathers are light.
2nd Imposition - Light is an adjective.
Feathers are adjectives.

Feathers is first used as an adjective and then as a noun (when, ironically, it is called an adjective).
Term
Second intention
 Definition
Of logic
Term
Second imposition
 Definition
Of grammar
Term
First imposition and first intention
 Definition
Of reality
Term
Zero imposition
 Definition
Of phonetics and spelling
Term
Fallacy with grammar used in two impositions
 Definition
Carry is a verb.
Verb is a noun.
Carry is a noun.

Verb shifts from first to second imposition
Term
Valid syllogism with grammar
 Definition
Sing is verb.
A verb has tense.
Sing has tense.
Term
Secundum quid
 Definition
Assumes that a proposition true in certain respects is true absolutely
Term
Fallacy of consequent
 Definition
There are two types of material fallacy of consequent:

1. Positing the consequent - Falsely assumes that because a consequent follows upon the antecedent, the antecedent must follow upon the consequent.

If it rains, the ground is wet.
The ground is wet.
It rained.

2. Sublating the antecedent - Falsely assumes that from the contrary of the antecedent the contrary of the consequent must follow.

If it rains, the ground is wet.
It did not rain.
The ground is not wet.
Term
Begging the question
 Definition
1. Tautological argument:

Shakespeare is famous because his plays are known all over.

2. The shuttle argument:

The boy is insane. Why? Because he murdered his mom. Why? Because he's insane.

3. Arguing in a circle:

Shuttle argument plus additional propositions.

4. Question-begging epithet:

Using a phrase that assumes the point to be proved.
Term
Induction
 Definition
The derivation of general propositions from individual instances.

The apprehension of the cause common to a number of observed facts.
Term
4 causes
 Definition
1. Efficient cause - the agent and instruments.

2. Final cause - the end or purpose that moved the agent. It is first in intention, last in execution.

3. Material cause - that out of which a thing is made.

4. Formal cause - the kind of thing which is made; its essence.
Term
KRegressive syllogism
 Definition
Links induction to deduction.

Seeks the cause of natural phenomena, a middle term, which is the formal cause of the relation of the terms in the conclusion of the syllogism.

So we see S is P, and we posit that S is P because of M. We want M to be the only antecedent of P so that M is P and P is M. So we want to say
Pif S is M
it is P
and if S is P
it is M.

If so we get this regressive syllogism:

S is P.
P is M.
Therefore S is M.

So

If S is M, it is P.
But S is M.
Therefore S is P.
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